Generalized Elliott-Yafet theory of electron spin relaxation in metals: the origin of the anomalous electron spin life-time in MgB2

The temperature dependence of the electron spin relaxation time in MgB2 is anomalous as it does not follow the temperature dependence of the resistivity above 150 K, it has a maximum around 400 K, and it decreases for higher temperatures. This violates the well established Elliot-Yafet theory of electron spin relaxation in metals. We show that the anomaly occurs when the quasi-particle scattering rate (in energy units) becomes comparable to the energy difference between the conduction- and a neighboring band. We find that the anomalous behavior is related to the unique band structure of MgB$_2$ and the large electron-phonon coupling. The saturating spin-lattice relaxation can be regarded as the spin transport analogue of the Ioffe-Regel criterion of electron transport.